INDUSTRIAL A N D ENGINEERING CHEMISTRY
1994
According to the authors cited the heat transfer process is described by the equations:
These same equations apply to the mass transfer process. The simplest set of initial and boundary condiTions is starting with a uniform temperature, 0, of bed and flo\virig fluid and changing the inlet temperature at zero time to To: The solutions for this case, integrals containing Bessel functions, have been evaluated by numerical or graphical methods. Schumann (6) and Furnas ( 2 ) have given tv-o sets of curves
Equations 3 and 1,although approximations, are considerably more accurate than the drawings given by Furnas ( 2 ) ; the ~ d i nates of the Furnas dravings are sometimes subject to errors over 0.01. ;\loreover, the Furnas curves do not allow easy interpolation for intermediate Y values, nhich problem does not# arisr any longer. The insufficiency of rhe Furnas curves for u8c in regions of l o w concentratioii is stressed by IClotz (4). X nomog~aph(Figure 2) is based on Equation 3. It has parallel and equidistant’ scales on which are indicated
Tj T and -’
as functions of Z for a numbtir of values of Y To ranging from 1to 500. Figure 1 s h o w such curves for Y = 2, 4, and 8 (full lines) The
sholving
Vcl. 40, No. 1,o
To
~
most rapid change of the ordinates takes place in the neighborhood of Z = Y . Also shon-n in Figure 1 is the curve (brolwn line) representing
!r To l/z
[I
1
dr
iz
- .iY
J
inverse
r
\
.
.
of the rrroi functlon of
As is cviderit from Equations 3 and 4 the same noinogrqh 7‘ can be uwd l o give the --!values---that is, by jiiterehangi~igZ 2’0
=
e-‘d2&
-a
+ erf(v‘z
the
- -d/r)i
(2)
and Y and subtracting the integral from unity. This is done by turning Figure 2 upside doim arid reading the other set of smbscripts. Thus, Y = 10 and Z = 12 correspoiids to 7 2 j = 0.70, but also
where e r f ( p ) represents the error function or prohability integral
To 1 ‘e
an approximation nhich has been used by Walter (8).
T/ T - and curves are very similar to this To To latter curve and about 112 unit’of 2 at either side of it. It is seen tha,t the
rr,
Z = 1 0 a n d Y =12to--Oo.3Cu. TQ For values of Y aiid Z , higher than those indicated OIL Figure 2 the reader may easily calculate further scales to t,he nomograph. However, the _ _error ~ _ _integral vrith the simpler upper limit. of integration d.Z - 4 Y or l / Z .- 41’ thvn should be 7’ 7‘ a good appros.matiori for 2 arid ;
